ADVANCED THREE-DIMENSIONAL TWOPHASE FLOW SIMULATION TOOL FOR
APPLICATION TO REACTOR SAFETY
CO-ORDINATOR
Dr. H. PAILLERE
CEA Saclay, DEN/DM2S/SFME
F-91191 Gif-sur-Yvette Cedex
FRANCE
Tel: +33.1.69.08.84.09
Fax: +33.1.69.08.82.29
LIST OF PARTNERS
1.
2.
3.
4.
5.
6.
7.
CEA Saclay and Grenoble, France
EDF Chatou, France
JRC Ispra, Italy
GRS Garching, Germany
MMU, United Kingdom
VKI, Belgium
PSI, Switzerland
CONTRACT No: FIKS-CT-2000-00050
EC Contribution:
Total Project Value:
Starting Date:
Duration:
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EUR 799 723
EUR 1 888 691
01/09/2000
39 months
CONTENTS
LIST OF ABBREVIATIONS
EXECUTIVE SUMMARY
A. OBJECTIVES AND SCOPE
B. WORK PROGRAMME
B.1 Critical evaluation and limitations of TH relationships and closure laws for 3D twophase flow models
B.2 Experimental and analytical work in support of TH analysis of 3D two-phase flow
B.3 Set-up of data structure and I/O formats for 3D module components
B.4 Development of advanced numerical methods for 3D simulation of two-phase flow
B.5 Industrial validation of milestones
B.6 Preparation of exploitation by industrial code developers and users and dissemination
C. WORK PERFORMED AND RESULTS
C.1. Hyperbolic schemes for nearly incompressible two-fluid flow: the phase separation
test case
C.2 Hyperbolic schemes for strongly compressible two-phase flow: the Super Canon test
case
C.3 Experimental data for multi-dimensional bubbly flow code validation
C.4 Coupling of fluid dynamic codes (system / multi-dimensional)
C.5 Dissemination of results and exploitation of results
CONCLUSIONS
REFERENCES
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LIST OF ABBREVIATIONS
AUSM
Advection Upwind Splitting Method
CEA
Commissariat à l’Energie Atomique
CFD
Computational Fluid Dynamics
EDF
Electricité de France
FVS
Flux Vector Splitting
GRS
Gesellschaft für Anlagen und Reaktorsicherheit
JRC
Joint Research Centre
LWR
Light Water Reactor
MMU
Manchester Metropolitan University
PSI
Paul Scherrer Institute
RDS
Residual Distribution Scheme
SCM
Split Coefficient Matrix
TH
Thermal-Hydraulics
VFFC
Volumes Finis à Flux Caractéristiques
VKI
Von Karman Institute for Fluid Dynamics
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EXECUTIVE SUMMARY
The ASTAR project was officially launched together with the EUROFASTNET
(project FIKS-CT-2000-20100) concerted action project on September 1st, 2000, and for a
duration of 36 months (extended to 39 months). The main objective of the ASTAR project
was to substantially enhance the three-dimensional two-phase flow prediction capabilities of
current Thermal-Hydraulic (TH) codes for safety relevant phenomena in present or future
innovative Light Water Reactors (LWRs) (eg. flow instabilities, steep gradients, critical heat
flux, etc), by laying the scientific and technical basis for a new generation of codes for
improved multi-dimensional two-phase flow simulation. This aim was to be achieved by
further development and adaptation of state-of-the-art numerical techniques for transient
two-phase flows allowing a high resolution of complex multi-dimensional flow processes,
while taking into account industrial requirements such as code robustness and accuracy. It
must be emphasized that successful simulation of physical diffusion and transfer processes
can only be achieved by combining such models with high resolution schemes whose
numerical diffusion is at least an order of magnitude lower than the physical diffusion. This is
not possible with the present generation of codes whose numerical methods, though extremely
robust, are overly diffusive and only first order accurate in space or time. These codes are also
essentially one-dimensional in nature.
The major task of the project was the development and verification of new multidimensional (1D,2D,3D) Thermal-Hydraulic code module components which are expected to
overcome many of the deficiencies and limitations of present TH-code like CATHARE,
ATHLET, TRAC or RELAP5, which have been identified and documented for a number of
years in OECD/CSNI workshops dedicated to thermal-hydraulic codes [1,2]. Enhancing the
three-dimensional modeling capability of existing system codes is another objective of the
ASTAR project, and as a proof of feasibility, a coupling between the multi-dimensional
module component (FLUBOX) and the existing system code ATHLET was performed in the
frame of this project. Concerning the verification of the improved prediction capabilities, a
number of numerical and physical benchmark calculations have been performed including test
cases of industrial interest such as bubble plume flows (for which a well instrumented
experiment was conducted at PSI to yield two-phase flow field measurements for 3D model
development and code validation), counter-current flows, natural convection and
boiling/condensation in large water pools or gravity-driven flows at low (near atmospheric)
pressure. Comparisons of calculations using existing methods (known as elliptic or pressurebased methods) such as found in the commercial CFD software CFX or the newly developed
CEA/EDF NEPTUNE-3D code were also made, so as to illustrate the clear benefit that the
new methodologies can bring. These benchmark cases are extracted from a list of flow cases
which the industrial partner, EDF, regards as being important challenges for two-phase flow
codes – and related to issues of safety and performance evaluation. Furthermore, it is also
believed that no single method can satisfactorily resolve all these benchmark problems, and
that alternatives to the current simulation technology have to be developed.
This synthesis report describes the work program and the different work packages of the
project. Difficulties that were encountered, as well as technical achievements are described.
Dissemination of the work through publications and open workshops are also described.
Finally conclusions concerning the ASTAR project and future prospects that would make use
of the ASTAR deliverables are made.
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A. OBJECTIVES AND SCOPE
One of the major conclusions from the OECD/CSNI "Workshop on Transient
Thermal-Hydraulics and Neutronics Codes Requirements " in Annapolis (1996) as well as in
Barcelona (2000) (Ref.[1,2]) was that existing thermal-hydraulics codes used in the nuclear
industry no longer represent the present state-of-the-art in physical and numerical modeling
and do not make use of the increased performance of present computer hardware. Specific
code deficiencies identified include the prediction of flows with steep parameter gradients
(e.g. two-phase mixture levels), strong thermal non-equilibrium effects, counter-current flow
conditions, critical (choked) flow conditions, transients conditioned by low driving heads like
natural convection, stratification in large water pools, or general three dimensional flow
phenomena. All these deficiencies are a consequence of oversimplified modeling of complex
two-phase flow processes and consequential drawbacks and limitations of the numerical
methods used in those codes.
These deficiencies have motivated the development of a new class of two-phase flow
methods (Ref.[3-10]), which may be seen as extensions of high resolution numerical schemes
used for single-phase gas dynamics (see (Ref.[11]) for a comprehensive review), building on
well-recognized techniques such as wave decomposition and upwind differencing techniques.
Just as their single-phase counterparts, these schemes are characterized by low numerical
diffusion, high resolution capture of shocks and sharp contact discontinuities and conservation
properties through a finite volume formulation. For non-equilibrium two-phase flow,
however, this numerical technology has not been thoroughly evaluated and compared to the
less accurate though more mature numerical methods at the heart of today’s thermal-hydraulic
two-phase flow codes such as CATHARE (Ref.[12]) or ATHLET (Ref.[13]). The ASTAR
project aimed precisely at further improving the accuracy and robustness of the new twophase flow methods, together with systematic evaluation and benchmarking, on a series of
test-cases covering a wide range of flow regimes, as well as on a specially designed bubbly
flow experiment, fully instrumented for validation of field codes. This is of course only the
first step in the validation process.
During the course of the project, multi-dimensional modules were further developed
and improved. These components are modules of existing thermal-hydraulic or CFD codes
developed by the partners (for example, TRIO_U at CEA, SATURNE at EDF, ATFM at JRCIspra or FLUBOX at GRS), and dedicated to the modeling of two-phase flow. Table I
summarizes the status of knowledge and the expected benefits to be gained from the project as
identified at the beginning of the project, and the achieved progress by the end of the project.
B. WORK PROGRAMME
The work program consists of in-house numerical developments performed on the
partners’ codes (at the start of the project these were: at CEA, TRIO_U; at EDF, SATURNE;
at JRC, ATFM; at GRS, FLUBOX), experimental work performed at PSI in the LINX
facility, and validation and analysis activities. Besides the management work-package, the
work was organized in 6 work-packages:
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B.1 Critical evaluation and limitations of TH relationships and closure laws for 3D twophase flow models
WP1 was concerned with the critical evaluation of the state-of-the-art in 3D transient
two-phase flow, and limitations of present models with respect to interfacial transfer
processes, transition from two-phase to single phase flow, etc. The SOAR was produced
jointly by the ASTAR and the EUROFASTNET consortia. A common basis for the physical
modeling of two-phase flow was adopted by the ASTAR partners, based on the equal pressure
two-fluid model used in many system codes (CATHARE, ATHLET, RELAP5, TRAC), with
added differential terms (virtual mass, interfacial pressure correction) to render the model
hyperbolic (Ref.[14-19]). Generic constitutive closure laws for interfacial drag for example
were also agreed. A selection of numerical and physical benchmark problems of industrial
interest was also made which specifies the physical models to be used, and thus allows to
compare the different characteristic-based upwind schemes developed in WP4, and evaluate
their numerical accuracy and robustness.
B.2 Experimental and analytical work in support of TH analysis of 3D two-phase flow
WP2 dealt with comprehensive experiments in the LINX facility of PSI, focusing
mainly on the bubbly flow regime. These experiments, required advanced measurement
techniques (double contact optical probe, PIV, electromagnetic velocimeters) and have
provided a valuable data-set for validation of multi-dimensional simulation tools.
B.3 Set-up of data structure and I/O formats for 3D module components
WP3 was meant to investigate the feasibility of developing generic modular
components, which could be shared and coupled to the different partners’ codes, by setting-up
a common data-structure and designing suitable input/output formats. Difficulties linked to
the different programming languages used (F77, F90, C, C++) were encountered which could
not be solved in the framework of the project. However, a recommendation to use a common
exchangeable data format, the CFD General Notation System (CGNS, http://www.cgns.org )
was adopted by all partners for future developments. CGNS was actually implemented in the
GRS code FLUBOX.
B.4 Development of advanced numerical methods for 3D simulation of two-phase flow
WP4 dealt with the developments and improvements of the numerical techniques: low
diffusion upwind differencing based on Riemann-solver techniques (Roe solver,
Characteristic Flux VFFC scheme, Flux Vector Splitting scheme, Residual Distribution
Scheme, Advection Upwind Splitting Method), specific treatment for non-conservative terms,
source terms and low Mach number effects, phase disappearance and implicit time-integration
algorithms. A scalar convection-diffusion equation for modeling of interfacial area
concentration transport was also implemented in the JRC ATFM code, to evaluate the effect
of coupling of such an equation to the two-fluid model, as well as to assess its potential with
respect to dynamic flow regime modeling.
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B.5 Industrial validation of milestones
WP5 was concerned with the verification and validation of the numerical methods on
the set of benchmark problems selected in WP1. Continuous feed-back on the development
phase (WP4) took place as the numerical methods were applied to the different test cases.
Comparisons with elliptic solvers (as in the commercial CFX code or the NEPTUNE code)
were also made. Unfortunately, the simulation of the LINX experiments with hyperbolic
methods could not be fully performed within the project, as the work on benchmark definition
and comparison took more time than anticipated, and so results have only been compared
qualitatively to the experimental data.
B.6 Preparation of exploitation by industrial code developers and users and
dissemination
WP6 focused on the dissemination of the results and the preparation of exploitation by
industrial code developers and users. For the latter, strategies for coupling the 3D modular
components to existing system codes such as ATHLET were investigated by GRS.
Concerning the dissemination aspects, a web-site was set up (http://www.grs.de/astar ) and an
open work-shop was also organized to give visibility to the work and to get feed-back from
the scientific world (see web site for details). Finally, a link with the ECORA project
(http://domino.grs.de/ecora/ecora.nsf ) was also made, in terms of an ASTAR contribution to
the ECORA Best Practice Guidelines, based on the experience gained in WP5.
The work program was modified towards the end of the project, through a contract
amendment, to take into account a reduced participation of CEA due to an internal decision to
stop the development of two-phase flow models in the TRIO_U code and to develop instead
together with EDF the NEPTUNE multi-dimensional solver. More work was carried out by
GRS, on the investigation of coupling strategies between a system code and a multidimensional module.
C. WORK PERFORMED AND RESULTS
In this section and because of lack of space, only some of the main achievements of
the project are illustrated and commented. The experimental results represent a unique set of
data for the validation of multi-dimensional bubbly flow. The results of the numerical
benchmark problems prove the feasibility of the numerical methods developed in the project,
and show that they provide a sound basis for the development of robust and accurate schemes
for multi-phase flow.
C.1. Hyperbolic schemes for nearly incompressible two-fluid flow: the phase separation
test case
This is an isothermal transient test case to investigate gravity-induced phase separation
and related counter-current flow conditions. It tests the ability of the methods to predict
counter-current flow conditions as exist in many reactor safety-related transients. Initial
conditions represents a vertical pipe of height L = 7.5 m filled with a homogeneous two-phase
mixture of specified void fraction  = 0.5. The specific challenge here is the prediction of
two steep void waves traveling simultaneously from the top and bottom ends into the pipe,
g
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which, when meeting at the middle section, results in the formation of a sharp interface (liquid
level) after phase separation is complete. For the flow velocities in the quasi-stationary middle
section of the pipe, as well as for the propagation of the void waves, an analytical solution
exists allowing direct comparison with the CFD calculations. The pressure remains close to
the initial value of 1 bar and temperature changes are negligible. Important modeling issues
are the interfacial forces including interfacial drag, pressure forces and virtual mass effects.
Heat and mass transfer, lift forces, wall friction and turbulent diffusion effects are ignored.
Interfacial drag is modeled by a simple law based on relative phase velocity (squared). This
test proves that hyperbolic methods, though designed to deal with highly compressible flow,
can successfully solve nearly incompressible flow.
C.2 Hyperbolic schemes for strongly compressible two-phase flow: the Super Canon test
case
From the Super-CANON test program, an experiment has been selected with a rather
high initial pressure (p = 150 bar) and a temperature of 300 oC (equivalent to a sub-cooling of
42 deg C). The test consists in a very fast depressurization of the contents (sub-cooled hot
water) of a horizontal tube 4.389 m long and 100 mm internal diameter, by opening a ''break''
equivalent to 100 % pipe area. During the first 10 ms of the transient, the governing
phenomena are the fast propagation of an expansion (rarefaction) wave into the pipe and the
incipient boiling (flashing). The later period of the transient is characterized by the possible
occurrence of critical flow conditions at the pipe exit and strong mechanical disequilibrium
between the phases. The predicted results depend strongly on the physical modeling of the
flashing phenomenon, the mixture speed of sound and the occurrence of choked flow
phenomena. This test provides a strong coupling between the flow and phase change
(evaporation) processes. Figure 2 shows that no specific problems were encountered in
predicting the fast depressurization with either the Flux Vector Splitting (FVS), the Split
Coefficient Matrix (SCM) or the Roe methods. The temporary occurrence of critical flow
conditions (choking) at the pipe exit is internally handled as a condition when the slowest
pressure wave propagation velocity becomes zero. Some remaining differences between the
predictions and measured pressure data, as shown in Figure 2 are the result of the specific
modeling of the evaporation rate which governs the whole blow-down process. This tests
shows that hyperbolic solvers can successfully solve highly compressible two-phase flow with
phase change and heat transfer.
C.3 Experimental data for multi-dimensional bubbly flow code validation
Within the ASTAR project, experiments on bubble plumes have been carried out in
the LINX test facility at PSI (see Figure 3). Although bubble columns have many practical
applications, the tests were not aimed at simulating a particular situation, rather they were
performed under well controlled initial and boundary conditions to provide a database for
code improvement and validation.
Isothermal tests have been carried out by injecting air into the bottom of a cylindrical
liquid pool through a specially designed circular injector containing 716 calibrated needles.
The carefully chosen gas injection rates and gas superficial velocity range correspond to the
discrete bubbly flow regime assuming that bubble coalescence and break-up effects remain
low. The air injector enables the creation of a broad, axis-symmetric bubble plume with an
average bubble diameter of about 3 mm and with large liquid recirculation zones around it.
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The tests were carried out following a test matrix in which parameters such as gas injection
rate and water level were varied.
To investigate specific two-phase flow parameters in the plume, multidimensional
measurements have been carried out. A particle image velocimetry (PIV) set-up was used to
measure 2-dimensional liquid- and bubble-velocity fields in a vertical plane. Double-tip
optical probes were used for local void-fraction measurements giving information also on
bubble size and interfacial area concentration. Some measured average void-fraction
distributions are depicted in Figure 4 showing the rise in the void fraction values for
increasing gas injection rates. Two corresponding average velocity distributions, also shown
in the figure, reflect a similar trend for both the liquid and bubble velocities. Corresponding
calculations are presently underway and comparisons with measured data will be included in
future publications.
The selected experiments performed in the LINX facility are genuinely 3-dimensional
in nature. During the start-up of the test, a bubble plume rises upward and, after reaching the
free surface, a steady (time-averaged) flow pattern is established. Depending on the relative
height of the liquid level, flow instability may develop characterized by a periodic oscillation
of the bubble plume (meandering flow pattern). A qualitative picture is given in Figure 5 (left)
showing the void distribution and velocity fields for gas and liquid calculated by the FVS
method of JRC using a quasi 2-dimensional grid with 2500 hexagonal cells. The calculation
clearly shows the recirculation pattern in the liquid pool and gas disengagement at the mixture
level free surface at about 1.0 m. Comparison with experimental data and computations with
elliptic solvers (NEPTUNE solution, shown right) are discussed in (Ref.[22]).
C.4 Coupling of fluid dynamic codes (system / multi-dimensional)
Thermal-hydraulic system codes for the fluid flow simulation in nuclear power plants (e.g.
ATHLET (Ref.[13])) consist of a network of one-dimensional objects. These objects simulate
pipes, pumps, pressurizers, the lower plenum, the reactor core, etc. Each facility component
and consequently the complete power plant facility can be assembled from these basic
objects. In situations where multidimensional effects become important, multidimensional
objects must be added to the network of the one-dimensional objects. The multidimensional
object might be any multiphase CFD code. The coupling of multidimensional objects with the
one-dimensional network of a system code consists of mainly three tasks.
o The first task is the exchange of the relevant data common to both systems. For this
one needs an interface for the data exchange between the differently structured
programs.
o The second task is the physical coupling. The programs may use different physical
models for the simulation of the fluid flow (e.g. in two-phase flow the models range
from homogeneous models to fully separated two-fluid models). Another problem is
the different spatial dimension (1-d and multi-d) of the approximation. Depending
upon technical requirements meaningful connections must be established. Finally the
different numerical spatial resolution might be a problem (e.g. staggered or nonstaggered grids).
o The third task is the efficient solution of the coupled system. The fluid flow in the
network of one-dimensional and multidimensional objects is described by systems of
nonlinear time-dependent ordinary differential equations. For both systems there exist
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efficient implicit solution methods. But the coupled system must be solved implicitly
also, otherwise it will suffer from Courant limit restrictions. The problem size of the
combined system is the sum of the problem sizes of the separate systems, and the
matrix of the linear system of the combined problem is accordingly upsized. Hence,
much larger linear systems of equations than that of the separate systems must be
solved.
In a prototype coupling of ATHLET and FLUBOX performed in the framework of the
project, it was shown how the combined system can be solved in an efficient way [20], where
the solution process of the implicitly coupled combined system maintains the solution
methods for each separate system. Figure 6 illustrates this coupling, with an application to the
calculation of the flow in the downcomer of the UPTF.
C.5 Dissemination of results and exploitation of results
The results of the ASTAR project have been published in the open literature, whether
on an individual basis or as a result of a joint project (Ref.[21,22]). A workshop was also
organized in Sept. 2003 to disseminate the results to the scientific community (see the project
web page, http://www.grs.de/astar ). The results of the project were published in the
proceedings of the FISA-2003 Symposium (http://www.cordis.lu/fp5-euratom/src/evfisa2003.htm ) as well as in a special issue of Nuclear Engineering and Design (Ref.[23]). In
terms of exploitation of results, GRS plans to continue the development of the FLUBOX code
as its multi-dimensional two-phase flow calculation tool. At CEA and EDF, the development
of hyperbolic discretization schemes will continue in the framework of the NEPTUNE
project, in the OVAP module. This work may be the subject of European involvement in the
NURESIM integrated project which is being envisaged.
CONCLUSIONS
The ASTAR project came to an end in November 2003. During its three year course,
progress has been made in the numerical solution of two-fluid flow problems using
characteristic-based methods. Individual efforts initiated in the different partner organizations
were combined to make further progress and improvements possible. More could certainly
have been done if the developments had been performed in a single code platform or with
easily exchangeable modules. This is a difficulty that will have to be overcome in future
projects dealing with inter-institutional code development. The benchmarking exercises
performed in the project were difficult to define precisely, but proved important to separate
the effect of the physical models from the effect of the numerical discretization technique, and
to establish the level of accuracy and robustness of the different methods. Comparisons with
standard solvers such as those of CFX or the elliptic NEPTUNE code have shown that the
hyperbolic schemes can deal with both compressible and nearly incompressible flow. More
needs to be done on the side of validation however, both in terms of multi-dimensional flows
and other flow regimes. The fact that most of the techniques developed in the ASTAR project
work on unstructured grids should facilitate their application to complex geometries. The
valuable experimental data set produced in the ASTAR project on bubbly flows should be
exploited in the near future.
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REFERENCES
[1] Proc OECD/CSNI Workshop on Transient Thermal-Hydraulic and Neutronic Codes
Requirements, Annapolis, Md, USA, 5-8 Nov. 1996, NUREG/CP-0159,
NEA/CSNI/R(97)4.
[2] Proc. OECD/CSNI Workshop on Advanced Thermal-Hydraulic and Neutronic Codes,
Barcelona, Spain, April 10-13, 2000.
[3] TOUMI, I., KUMBARO, A., 1996, An Upwind Numerical Method for Two-Fluid TwoPhase Flow Models, Journal of Computational Physics, 124, pp.286-30.
[4] GHIDAGLIA, J.M., KUMBARO, A., LE COQ, G., 2001, On the numerical solution to
two fluid models via a cell-centred finite volume method, European Journal of Fluid
Mechanics, B/Fluids, 20, No.6, pp.841-867.
[5] PAILLERE, H., CORRE, C., GARCIA-CASCALES, J.R., 2003, On the extension of the
AUSM+ scheme to compressible two-fluid models, Computers and Fluids, 32, pp. 891916.
[6] ROMSTEDT, P., 1990, A Split-Matrix Method for the Numerical Solution of Two-Phase
Flow Equations, Nuclear Science and Engineering, 104, pp.1-9.
[7] GRAF, U., 1993, A Numerical Solution Method for Multidimensional Hyperbolic TwoPhase Flow Models, Proceedings 3rd Nuclear Simulation Symposium, Schliersee,
Germany
[8] STAEDTKE, H., WORTH, B., FRANCHELLO, G., 2001, On the hyperbolic nature of
Two-phase Flow Equations: Characteristic Analysis and Related Numerical Methods,
Godunov Methods: Theory and Applications, (Ed. E. F. Toro), Kluwer Academic/Plenum
Publishers, New York.
[9] STAEDTKE, H., BLAHAK, A., WORTH, B., 1997, Modelling of Interfacial Area
Concentration in Two-Phase Flow Systems, 8th Int.l Meeting on Nuclear Thermal
Hydraulics, Kyoto, Japan, September 30 - October 4, 1997.
[10] STAEDTKE, H., FRANCHELLO, G., WORTH, B., 1995, Numerical Simulation of
Multidimensional Two-phase Flow based on Flux Vector Spliiting, 7th International
Meeting on Nuclear Thermal Hydraulics, NURETH7, Saratoga Springs, NY, USA, Sept.
1995.
[11] TORO, E.F., 1999, Riemann Solvers and Numerical Methods for Fluid Dynamics,
Springer, Berlin Heidelberg.
[12] BESTION, D., 1990, The physical closure laws in the CATHARE code, Nucl. Eng.
Design, 124, pp.229-245.
[13] TESCHENDORFF, V., et. al., ATHLET Home Page,
http://www.grs.de:8081/garching/athlet/athlet.htm , 2003
[14] BOURE, A., 1975, On a Unified Presentation of the Non-Equilibrium Two-Phase
Flow Models, Proceedings of ASME Symposium, New York.
[15] DELHAYE, J.M., ACHARD, J.L., 1976, On the Averaging Operators Introduced in
Two-Phase Flow Modelling, Proceedings of CSNI Specialist Meeting on Transient TwoPhase Flow, Toronto.
[16] DREW, D., CHENG, I.,, LAHEY, R.T., 1979, The Analysis of Virtual Mass Effects in
Two-phase Flow, International Journal of Multiphase Flow, 5, No. 4, pp.233-242.
[17] DREW, D., LAHEY, R.T., 1979, Application of General Consitutive Principles to the
Derivation of the Multidimensional Two-phase Flow Equations, International Journal of
Multiphase Flow, 5, pp.243-264.
[18] HEWITT, G., et al, 1986, Workshop on Two-phase Flow Fundamentals as published
in Multiphase Science and Technology, Vol 6.
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[19] ISHII, M.,, 1975, Thermodynamics of Two-Phase Flow, Eyrolles, Paris.
[20] GRAF, U., 1998, Implicit Coupling of Fluid-Dynamic Systems: Application to
Multidimensional Countercurrent Two-Phase Flow of Water and Steam, Nuclear Science
and Engineering, 129, 305-310
[21] STAEDTKE, H., et al., The ASTAR project: status and perspective, 10th Int. Topical
Meet. Nuclear Thermal-hydraulics NURETH-10, Seoul, Korea, 6-13 October, 2003
[22] MIMOUNI, S., et al., ASTAR: benchmarking of test cases, ASTAR International
Workshop on ”Advanced Numerical Methods for Multidimensional Simulation of Twophase Flow”, September 15-16, 2003, GRS Garching, Germany
[23] STAEDTKE, H., et al., Advanced three-dimensional two-phase flow simulation tools
for application to reactor safety (ASTAR), Nuclear Engineering and Design, to be
published (2005)
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TABLES:
Table I. Two-phase CFD codes used and developed further in the ASTAR project
Partner
Physical model
Numerical method
CEA
Name twophase flow
CFD Code
TRIO_U
Two-fluid 1-pressure
model, interfacial pressure
correction to render
hyperbolic
Approximate Riemann
Solver (Roe or VFFC
schemes, unstructured
finite volumes) in OVAP
module. C/C++.
Also elliptic method (ICE)
available in TRIO_U.
EDF
SATURNE
Two-fluid 1-pressure
model
JRC
ATFM
Two-fluid 1-pressure
model, virtual added mass
to render hyperbolic
Elliptic method
(SIMPLEC algorithm,
collocated unstructured
finite volumes). Also a
hyperbolic scheme
(VFFC). Fortran 77.
Flux Vector Splitting
method (unstructured
finite volumes).
Fortran 77
GRS
FLUBOX
Two-fluid 1-pressure
model, interfacial pressure
correction to render
hyperbolic
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Split Coefficient Matrix
Method (Cartesian grids
only, finite differences).
Fortran 90.
Status at the
beginning of
project
3D solver
developed.
Incorporation of
physical
modeling terms
still missing.
1st order time &
space accurate
scheme. Implicit
time-integration
Two-fluid
air/water flow
only. No heat
transfer model.
2D unstructured
meshes. 2nd order
space & time
accurate scheme.
Implicit scheme.
2D solver with
physical
modeling terms.
Implicit timeintegration with
error control.
Expected status
at end of project
Achieved status at
end of project
3D solver
(hyperbolic &
elliptic methods)
for two-phase
flow with heat
transfer,
validated on
ASTAR
benchmarks
CEA/EDF:
Merge of
TRIO_U/OVAP
and
SATURNE/VFFC
into FLICAOVAP code
(hyperbolic
methods)
3D solver
(hyperbolic and
elliptic solvers)
validated on
ASTAR
benchmarks,
Energy equation
added, 2D solver
validated on
ASTAR
benchmarks
3D solver
validated on
ASTAR
benchmarks.
Coupling
exercise with
ATHLET code.
Development of
NEPTUNE-3D
based on
SATURNE
elliptic solver
(elliptic methods)
Energy equation
added, 2D solver
validated on
ASTAR
benchmarks
3D solver
validated on
ASTAR
benchmarks.
Coupling exercise
with ATHLET
code.
0.00
-0.2
0
FIGURES:
1
2
3
4
5
6
7
distance x [m]
0.50
0.50
t0
0.0
0.0
1
1
2
2
3
3
4
5
4
5
distance x [m]
distance x [m]
6
6
7
0.2
0.2
SCM method (GRS)
1.00
1.00
velocity
velocityug,ugu
, lu[m/s]
l [m/s]
AUSM method (CEA)
0.75
0.75
0.50
0.50
0.25
0.25
0.00
0.00 0
0
1
1
2
2
3
3
4
5
4
5
6
6
distance x [m]
distance x [m]
2
3
2
3
4
4
5
distance
3
4x [m]
distance x [m]
distance x [m]
5
6
5
6
7
6
7
-0.2
7
SCM method
FVS method
(JRC) (GRS)
CFX4 method (PSI)
SCM method (GRS)
t6
0.75
0.75
0.50
0.50
0.25
liquid
12
2
1
23
34
45
56
3
4
5
6
distance
x
[m]
2
3
4x [m] 5
distance
distance x [m]
distance x [m]
67
7
6
1
2
3
4
5
6
distance x [m]
0.25
12
2
1
23
34
45
56
3
4
5
6
2distance
3 x [m]4x [m] 5
distance
distance x [m]
distance x [m]
67
7
6
0.2
-0.2
0.50
0.25
0.25
void fraction [/]
velocity ug, ul [m/s]
2
3
4
distance x [m]
533563345
5
6
7
1
1
23
34
45
56
1
2distance
distance
3 x [m]4x [m] 5
67
7
6
7
0.1
0.0
-0.1
0
1
0.1
0.1
0.0
0.0
-0.1
-0.1
-0.2
12
-0.2
1
0
0
0.2
velocity
ug, ulug[m/s]
velocity
, ul [m/s]
0.50
AUSM method (CEA)
0
-0.1
-0.1
7
AUSM method (CEA)
AUSM method (CEA)
0.00
0.0
0.0
-0.2
7
AUSM method (CEA)
0.1 1.00
0.75
1.00
0.25
0.1
0.2
distance x [m]
0.50
1
1
CFX4 method (PSI)
0.2
0.75
0
0
0.1
-0.2 0.00
0
01
0.00
0
7
-0.1
-0.1
0.2
0.50
-0.1
0.25
-0.1
voidvoid
fraction
[/] [/]
fraction
velocity ug, ul [m/s]
void fractiong [/]
0
0.0
0.0
-0.2
SCM method
(GRS) (PSI)
CFX4 method
AUSM method (CEA)
CFX4 method (PSI)
1.00
1.00
0.00
0.1
7
0.75
0.0
0.0
0.50
-0.1
2
2
-0.2
7
0.75 1. Phase separation problem: time-evolution of void fraction, comparison between
Figure
0.75 and CFX code (elliptic method).
FVS, SCM, AUSM schemes (hyperbolic methods)
0.0
0.25
1
1
0.2
0.2
0.50
0
0
0.1
1.00
0.1 1.00
0.1
0.75
CFX4 method (PSI)
1.00
-0.1
-0.1
0.2
gas
-0.2 0.00
-0.2 0
01
0 0.00 1
0
7
7
0.0
0.0
-0.2
1
2
1
0.25
-0.2 0.00
-0.2 0
01
0 0.00 1
0
7
voidvoid
g [/]g [/]
fraction
fraction
0.00
0.00 0
0
void fraction [/]
void fractiong [/]
0.1
0.1
-0.1
-0.1
0.25
0.25
t0
0.00
0
0 0.00 1
0
voidvoid
g [/]g [/]
fraction
fraction
t7
0.25
0.25
t1
1.00
velocity ug, ul [m/s]
velocity ug, ul [m/s]
void fractiong [/]
void fractiong [/]
t1
0.75
0.75
t0
0.2
0.2
FVS method (JRC)
CFX4 method (PSI)
1.00
1.00
velocity
ug, ulug[m/s]
velocity
, ul [
-0.1
0.50
0.50
velocity
ug, ulug[m/s]
velocity
, ul [m/s]
0.25
0.0
0.75
velocity
ug, ulug[m/s]
velocity
, ul [m/s]
0.50
t7
1
voidvoid
g [/]
fraction
fraction
velocity ug, ul [m
void fractiong
0.75
2
3
4
distance x [m]
5
6
7
-0.2
0
1
0
1
v o id fr a c tio ng
p r e s s u r e [b
1
80
40
2
3
0 .7 5
2
0 .5 0
0 .2 5
1
3
0
0 .0
0 .1
0 .2
0 .3
0 .4
0 .0 0
0 .0
0 .5
0 .1
0 .2
tim e t [s ]
0 .3
0 .4
0 .5
tim e t [s ]
160
1 .0 0
F V S m e th o d ( J R C )
120
1 .0 0
v o id fr a c tio ng [/]
v o id fr a c tio ng [/]
r e a[b
p r epsrseusrseu [b
r]a r]
160
S C M m e th o d ( G R S )
120
1
2
1
80
80
40
2
3
40
3
0
0 .0
0
0 .0
3
0 .1
0 .2
0 .3
0 .4
0 .5
0 .1
tim e t [s 0] .3
0 .2
0 .4
0 .5
3
3
V Smme e
(JR
RC
S CFM
ththo odd ( G
S ))
0 .7 5
0 .7 5
2
0 .5 0
1
0 .5 0
0 .2 5
1
2
0 .2 5
0 .0 0
0 .0
0 .0 0
0 .0
0 .1
0 .2
0 .3
0 .4
0 .5
0 .1
0 .2tim e t [s
0 ].3
0 .4
0 .5
tim e t [s ]
tim e t [s ]
160
1 .0 0
S C M m e th o d ( G R S )
A U S M m e th o d ( C E A )
120
120
1
1 .0 0
ida cfrtio
a cntio[/]ng [/]
v o vido fr
g
p r epsr seusrseu[b
] a r]
r ea r[b
160
2
1
80
2
80
40
40
3
0
0 .0
3 .1
0
0
0 .0
0 .2
0 .1
0 .3
tim 0e .2t [s ]
0 .4
0 .3
0 .7 5
3
S C M m e th o d ( G R S )
3
A U S M m e th o d ( C E A )
0 .7 5
1
1
0 .5 0
0 .5 0
2
0 .2 5
2
0 .2 5
0 .0 0
0 .0
0 .0 0
0 .0
0 .5
0 .4
0 .1
0 .2
0 .3
tim 0e.2t [s ]
0 .1
tim e t [s ]
0 .4
0 .3
0 .5
0 .4
tim e t[s ]
160
1 .0 0
A U S M m e th o d ( C E A )
120
1 .0 0
R o e s c h e m e (C E A )
120
o idfr afrca tio
c tionng[/][/]
v ovid
p r e sp sr eusrseu [b
r e a[br ]a r ]
160
1
2
80
80
40
40
3
0 .0
0 .1
0 .2
0 .3
0 .4
0 .1
tim 0e.2t [s ]
0 .3
0 .4
A U S M m e th o d ( C E A )
0 .7 5
R o e s c h e m e (C E A )
0 .7 5
0 .5 0
1
3
0 .5 0
2
0 .2 5
1
0 .2 5
2
0 .0 0
0 .0
0 .0 0
0 .0
0
0
0 .0
3
0 .1
0 .2
0 .3
0 .4
0 .1
tim0e.2t[s ]
0 .3
0 .4
tim e t [s ]
tim e t [s ]
160
v o id fr a c tio n [/]
p r e s s u r e [b a r ]
1 .0 0
Figure 2: Fast depressurization
of pressure and void fraction, comparison
R o e s c h ecase,
m e ( C Etime-evolution
A)
120
R o e s c h e m e (C E A )
between FVS, SCM and Roe schemes
0 .7 5 and experimental results
80
40
3
0 .5 0
1
0 .2 5
2
0
0 .0
0 .1
0 .2
tim e t [s ]
533563345
0 .3
0 .4
0 .0 0
0 .0
0 .1
0 .2
tim e t [s ]
0 .3
0 .4
vent
liquid free
surface
pressure
vessel
(D=2 m)
spout
windows
recirculation
zone
plume
needle plate
(d=300 mm)
gas inlet
Figure 3: The LINX test facility
533563345
water level :
1.5 m (above injector)
measuring elevation:
55.2 cm (above injector)
4
air injection
rate:
60 nl/m
3.5
30 nl/m
0.7
0.6
15 nl/m
0.5
7.5 nl/m
vertical velocity [m/s]
Void fraction [%]
3
2.5
2
1.5
0.4
liquid 15nl/m
liquid 30nl/m
bubble 15nl/m
bubble 30nl/m
0.3
0.2
1
0
-25
-15
-5
0
5
r [cm]
water level :
1.5 m (above injector)
measuring elevation:
55.2 cm (above injector)
0.1
0.5
15
25
0
5
10
r [cm]
15
20
Figure 4. Radial void-fraction distribution for increasing air injection rate (left); liquid and
bubble velocity distributions for two corresponding injection rates (right).
Figure 5. left, 2-D calculation for the LINX facility, hexagonal grid with 3000 computational
cells (hyperbolic FVS method) ; right, 3-D calculation (void fraction) performed with the
NEPTUNE code (elliptic method)
533563345
Gik
ik
ATHLET COLD LEG (1D)
Y
X
Z
Figure 6. Coupling of a multidimensional module with a system code: prototype work
between ATHLET and FLUBOX, example of an application to the UPTF Test 6 case.
533563345